JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 81

Let the coefficients of the middle terms in the expansion of $\left(\dfrac1{\sqrt6}+\beta x\right)^4$, $(1-3\beta x)^2$ and $\left(1-\dfrac\beta2x\right)^6$, $\beta>0$, respectively form the first three terms of an A.P. If d is the common difference of this A.P., then $50-\dfrac{2d}{\beta^2}$ is equal to ______.